# Doppler Effect of an ambulance

1. May 29, 2010

### roam

1. The problem statement, all variables and given/known data

An ambulance is traveling at 72.0 km/h towards an intersection. Jim stops his car to give way to the ambulance as shown in the diagram below. In the diagram, the angle θ = 41.0 °.
The ambulance has a siren which produces sound at a frequency of 2.1 kHz. Assume the speed of sound in air is 335.0 m/s.

[PLAIN]http://img693.imageshack.us/img693/7959/amburightjimrest.gif [Broken]

What is the doppler shift (Δf = f ′ – f ) heard in the siren sound by Jim, when Jim and the ambulance are positioned as shown on the diagram above?

2. Relevant equations

General Doppler-shift expression: $$f'=\left( \frac{v+v_o}{v-v_s} \right)f$$

3. The attempt at a solution

$$f'=\left( \frac{v+v_o}{v-v_s} \right)f= \left( \frac{335}{335-72} \right)2.1=2.62$$

f'-f=2.62-2.1= 0.52

Why am I not getting the right answer? Does this have something to do with the angle? All the examples in my textbook deal with situations where the observer or the source are moving directly toward one another, there are no examples with angles. Any help is appreciated.

Last edited by a moderator: May 4, 2017
2. May 29, 2010

### Dweirdo

First, you have to convert km/h to m/s.
Next, does the source advance in the y direction?? does it advance in the X direction?
what is the source's velocity in y direction(if it has any..)?? what is the source's velocity in the X direction?
what should you plug in the equation?

3. May 29, 2010

### roam

The source is moving in the x direction but the sound that reaches the driver has both x and y component.

vx=335cos41=252.8
vy=335sin41=219.7

The resultant is:

$$\sqrt{252.8^2+219.7^2}=334.9$$

$$\frac{334.9}{334.9-20}2.1=1.27$$

then why do I still get the wrong answer?

4. May 29, 2010

### Dweirdo

the velocity of the source is 20 m/s to the left, no doubt about that.
the velocity of sound in air is 335 m/s still no doubt about that.
You need to take the component of the velocity in the direction connecting the ambulance with the car.
to get that component it's 20*cos41 and you'll get the right answer..

5. May 29, 2010

### roam

Thank you!!! I get it now!